An algorithm to determine the directional relationship between arbitrarily-shaped polygons in the plane

Unified Pairwise Spatial Relations: An Application to Graphical Symbol Retrieval

“…Approaches based on the Minimum Bounding Rectangle (MBR) [18,27,5,28,12] give more interesting relations as they also approximate shape and size of the object. The quality of the bounding rectangle depends on compactness 1 of the tile.…”

“…They can be either topological [10][11][12][13] or directional [14][15][16][17][18] in nature. Further, models are entirely depending on the characteristics of the studied objects as well as specific application driven needs for spatial relations, such as binary or metrical refinement: the level of detail in the expression of spatial predicates such as Left, Right etc., varies widely from one application to another [19] as does to the precision of the quantised information.…”

An approach to computing direction relations between separated object groups

“…A number of models for describing and/or computing direction relations have been proposed, including the conebased model (Peuquet and Zhan, 1987;Abdelmoty and Williams, 1994;Shekhar and Liu, 1998), the 2-D projection model (Frank, 1992;Nabil et al, 1995;Safar and Shahabi, 1999), the direction-relation matrix model (Goyal, 2000), and the Voronoi-based model (Yan et al, 2006). These models can compute direction relations between two single objects, but can not compute direction relations between two object groups.…”

“…-The cone-based model (Peuquet and Zhan, 1987) partitions the 2-dimensional space around the centroid of the reference object into four direction regions corresponding to the four cardinal directions (i.e., N, E, S, W). The direction of the target object with respect to the reference object is determined by the target object's presence in a direction partition for the reference object.…”

Directional Regions in Geographic Information Systems (GIS)

“…Routines to calculate the direction between two points or between a point and the nearest point on another feature are sometimes included in GIS software. In addition, some research has been directed at the determination of directional relationships among polygons (Peuquet and Zhan, 1987). However, functions to comprehensively determine directional relationships among objects (such as lines or polygons) or to create directional regions relative to a single object (point, line, or area) are not found in commercial products.…”